Similarities derived from 3-d nonlinear psychophysics: Variance distributions

Many-one mappings between stimulus properties and pairwise generated similarities are intrinsic to definitions of similarity. This of itself is not sufficient as a basis for predicting the variance associated with any single similarity judgment. An extension to cover this has to be made either by making ancillary assumptions about noise, or by using nonlinear models. The derivation of the variance of similarity judgments is made from the 3 process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter which represents the degree of a form of interdimensional crosscoupling